1. Technical Field
The electrical current which is supplied to a load, e.g. a three-phase electrical machine, is normally of equal amplitude in all the phases. The phase displacement between the currents is also normally the same and, in a three-phase network equals 120.degree.. In the cases of an unbalanced load, an interruption in one phase, or the appearance of an abnormal operating condition such as, for example, a single-phase or two-phase short-circuit, the phase currents will become unbalanced. It is generally known that three-phase electrical machines of many different kinds are sensitive to an unbalanced load and may be destroyed if the unbalanced load becomes excessive.
A measure of the degree of unbalanced load can be obtained by reference to the so-called negative sequence current, which is a symmetrical three-phase current with equal amplitude in all phases but with negative phase sequence. The actual unbalanced current caused by the unbalanced load being quantified consists of this negative sequence current with the addition of two other symmetrical three-phase currents; namely one with positive phase sequence and one with zero phase sequence. The three sequence currents may have different amplitudes. The negative sequence currents generate a stator magnetomotive force (mmf) having a negative phase sequence and with the same rotational speed as the stator field of the machine but with the opposite direction of rotation. This mmf therefore rotates relative to the rotor at a rate equal to twice the supply frequency. This leads to currents with twice the supply frequency being induced in the metallic parts of the rotor, for example in the damper windings. It is these induced higher frequency currents that may eventually damage the rotor if the negative sequence current is too large and subsists for too long a period of time.
To protect an electrical machine from damage caused by such an unbalanced load, a so-called negative current protection, based on a measurement of the negative sequence current, is therefore provided. In order to obtain a measure of the negative sequence current from the mains currents in question, presently known negative current protectors include a measuring device in the form of a filter containing resistors and inductances or capacitors. The present invention relates to a new method and a new device for obtaining a measure of this current without the use of R-, L- or C-components.
2. Description of the Prior Art
From a general point of view, the procedure adopted when resolving an unbalanced three-phase current in a network into a symmetrical negative and positive current system will be different depending on whether the network is grounded or not. If the network is not grounded, the unbalanced current may be resolved, as previously mentioned, into a negative and a positive sequence current, the negative sequence current having negative phase sequence and the positive sequence current having positive phase sequence relative to the network. FIG. 1 of the accompanying drawings illustrates an unbalanced load, and FIG. 2 thereof illustrates the corresponding positive and negative sequence currents and the phase sequences in the case of an ungrounded network.
When the network is grounded, an unbalanced load will, in addition, give rise to a zero sequence current, which means that the resolution will comprise a zero phase sequence system which in a three-phase system consists of three single-phase quantities which are equal in amplitude and phase. The resolution of a grounded network with an unbalanced load could be as shown in FIG. 3 of the accompanying drawings.
Since the phase currents of the negative sequence system are equal, it is only necessary to measure one of these currents. As will be described, in an ungrounded system the negative sequence current, or a signal proportional thereto, can be measured with the aid of two of the phase currents in the network in question. In a grounded system all the phase currents have to be measured in a special connection, to eliminate the zero sequence current, as will be clear from the following analysis given with reference to FIG. 8 of the accompanying drawings.
The resolving of the phase currents, to obtain a measure of the negative sequence current, takes place in accordance with a known procedure in a so-called negative current filter. Such a filter is described in the specification of U.S. Pat. No. 3,699,411. A modified negative current filter is illustrated in FIG. 4 of the accompanying drawings and will now be described in more detail. The filter shown in FIG. 4 comprises a resistor R.sub.1 in parallel with an inductance L.sub.1. The parallel connection is supplied with a current corresponding to the phase current I.sub.T, a voltage U.sub.1 thus appearing across the connection. Further, the filter comprises a series connection of an inductance L.sub.2 and a resistor R.sub.2, which is traversed by a current corresponding to the phase current I.sub.R. Across the series connection a voltage U.sub.2 appears. By a suitable dimensioning of the components included in the filter, it can be shown that the output signal U of the filter, when no negative sequence current exists, i.e. when the network is symmetrically loaded, is zero and that, when a negative sequence current exists, the output voltage U represents a signal proportional to the negative sequence current.
In a symmetrically loaded network, all the phase currents I.sub.R, I.sub.S and I.sub.T, as shown in FIG. 5 of the accompanying drawings, are equal in amplitude and displaced in phase 120.degree. with respect to each other. Taking I.sub.R as the reference phase, U.sub.2 is formed as the resultant of I.sub.R R.sub.2 in phase with I.sub.R and I.sub.R X.sub.L.sbsb.2, displaced in phase 90.degree. with respect to I.sub.R. Since X.sub.L.sbsb.2 is frequency dependent, the locus of I.sub.R X.sub.L.sbsb.2 is a straight line on which I.sub.R X.sub.L.sbsb.2 has been marked for the rated frequency f.sub.n as well as for 0.8.multidot.f.sub.n and for 1.2.multidot.f.sub.n.
Because of the current directions indicated in the filter of FIG. 4, in order to determine U.sub.1 it is necessary to start from the phase current -I.sub.T, that is, -I.sub.R &lt;120.degree.. The locus of U.sub.1 is a semi-circle, on the periphery of which have been marked, the end points of the vector U.sub.1 at the respective rated frequencies f.sub.n, 0.8.multidot.f.sub.n and 1.2.multidot.f.sub.n.
By suitable dimensioning and trimming, U.sub.1 will be equal to U.sub.2, and since U is the voltage between the end points of the vectors U.sub.1 and U.sub.2, U will be equal to 0.
On studying the conditions during unbalanced load, the negative sequence current diagram of FIG. 2 can be the starting-point. Taking I.sub.R- as the reference phase, the voltage U.sub.2 is formed, as shown in FIG. 6 of the accompanying drawings, in the same way as in the previously described symmetrical case. Because of the reversed phase sequence of the negative sequence system and the current direction of I.sub.T indicated in the filter of FIG. 4, it will be necessary also in this case to start from -I.sub.T-, that is, -I.sub.R &lt;240.degree.. The locus of U.sub.1 consists of the semi-circle shown in FIG. 6. The output signal U of the filter is clear from FIG. 6, and the absolute value of the vector is proportional to the negative sequence current and thus constitutes a measure of this current.
The current feed to the negative current filter of the type shown for an ungrounded system will be clear from FIG. 7 of the accompanying drawings. In addition to current transformers S.sub.R and S.sub.T, this figure also shows auxiliary current transformers M.sub.R and M.sub.T.
For a grounded system, in order to eliminate a possible zero sequence current, all the phase currents must be measured, which is done by means of current transformers S.sub.R, S.sub.S and S.sub.T (see FIG. 8 of the accompanying drawings). Auxiliary current tranformers M.sub.1 and M.sub.2 are also included and the connection of these is shown in FIG. 8.
Negative current filters, whether according to the above-mentioned U.S. Pat. No. 3,699,441 or the filters described here, suffer from certain drawbacks. As will be clear from FIG. 5, the filter will deliver an output voltage also in the case of a balanced load system when the frequency varies, since U.sub.1 and U.sub.2 are different. Also in the case of dynamic and transient changes in the network, the filter is able to deliver a signal without there being any negative sequence current in the network. Harmonics on the network may also result in the filter delivering an output signal because of different frequency responses in the three phases.
Such fault indications may give rise to unjustified alarm, blocking or tripping.
As will have become clear, the current in each phase in a system with unbalanced load can be resolved into a negative and a positive sequence component and possibly, if the system is grounded, into a zero sequence component. In the analyses shown in FIGS. 1 and 2, I.sub.R1 has been
resolved into I.sub.R+ and I.sub.R- with the angle .theta. between the components, as will be clear from FIG. 9 of the accompanying drawings. The relationship between I.sub.R1, I.sub.R+ and I.sub.R- can be described with the aid of the cosine theorem. For the S- and T-phases corresponding relationships arise so that a characteristic of the system is that .vertline.I.sub.R+ .vertline.=.vertline.I.sub.S+ .vertline.=.vertline.I.sub.T+ .vertline.=.vertline.I.sub.1 .vertline. and that .vertline.I.sub.R- .vertline.=.vertline.I.sub.S- .vertline.=.vertline.I.sub.T- .vertline.=.vertline.I.sub.2 .vertline. and that the phase angles between the resolved positive and negative sequence currents, respectively, are 120.degree.. For the R-phase, the following equation is valid: EQU I.sub.R.sup.2 =I.sub.1.sup.2 +I.sub.2.sup.2 -2I.sub.1 I.sub.2 cos .theta.
where
.vertline.I.sub.1 .vertline.=Positive sequence component and PA1 .vertline.I.sub.2 .vertline.=Negative sequence component.
Corresponding equations can be deduced for the S- and I-phases, which gives three equations with three unknowns, so that by making a current measurement of all the phase currents, it is possible to calculate both the negative and the positive sequence component as well as the angle .theta..